The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1
 0  X  0  0  X  X a*X a^3*X  0 2*X a^2*X  X a^2*X a*X a^2*X a^5*X a*X  X a*X 2*X a^6*X a^2*X  0 a*X  0  X 2*X a^6*X a^2*X a^2*X 2*X a^3*X  X a^5*X a^6*X a^6*X a^5*X a^6*X  X a^6*X a^5*X 2*X a*X 2*X a*X a*X  X a^2*X a^6*X  X  X a^7*X
 0  0  X  0 a^7*X a^6*X a*X 2*X  X a^6*X a^6*X  X a^3*X  X a^5*X  X a^2*X a^6*X a^5*X a^6*X a^5*X a^7*X a^5*X 2*X a^2*X  0  0  0 a^2*X 2*X 2*X a^2*X a^6*X a*X a^6*X a^7*X a*X a^6*X a*X a^5*X a^3*X  X a^7*X a*X a^5*X  X  X a^3*X a^7*X a^5*X  0  0
 0  0  0  X a^7*X  X a^5*X a*X a*X a^7*X 2*X a^7*X a^3*X a^2*X 2*X a^3*X a^6*X 2*X  X a^6*X a^6*X a*X 2*X  0  X a^6*X a^5*X a^6*X a^3*X  0 2*X a*X a^5*X a^3*X a*X a*X  0 a^7*X a^5*X a^2*X a^7*X 2*X a^7*X  X a^5*X a^3*X  0 a*X a^5*X a^7*X a^5*X a^3*X

generates a code of length 52 over F9[X]/(X^2) who´s minimum homogenous weight is 387.

Homogenous weight enumerator: w(x)=1x^0+592x^387+1144x^396+648x^400+1128x^405+10368x^409+888x^414+41472x^418+984x^423+616x^432+592x^441+416x^450+160x^459+40x^468

The gray image is a linear code over GF(9) with n=468, k=5 and d=387.
This code was found by Heurico 1.16 in 1.01 seconds.